The observation algebra of spatial pomsets

  • Gian Luigi Ferrari
  • Ugo Montanari
Selected Presentations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 527)


For sequential programming, the theory of functions provides a uniform metalanguage to describe behaviours by abstracting from the actual implementation of programs. For concurrent and distributed systems, instead, there is no well accepted metalanguage to describe the possible observations of the behaviour of programs. The proper treatment of observations is thus an important and complex issue of concurrency theory. In this paper we show that observations can be described in a uniform way by introducing certain algebras called observation algebras. They lift to an algebraic level the standard treatment of actions in the operational semantics of process algebras. Observations are described as terms of an algebra. As a consequence, we separate the control level (the operational semantics) from the data level (the observations). The chosen notion of observability can be obtained by suitably axiomatizing the operations of the observation algebra. We show how observation algebras can be naturally derived from process algebras. As a case study we consider Milner's CCS. We introduce an observation algebra for CCS and we show that the standard interleaving semantics can be obtained by axiomatizing the operations to yield actions. Furthermore, we give a complete axiomatization of an observation algebra whose elements are certain labelled partial orderings of events (pomsets) called Spatial Pomsets.


Normal Form Operational Semantic Sequential Composition Process Algebra Dynamic Logic 
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  1. [AB84]
    Austry, D. Boudol, G. Algebra de Processus et Synchronization, Theoretical Computer Science 30 (1), pp 91–131, 1984.Google Scholar
  2. [BC88]
    Boudol, G., Castellani, I., Concurrency and Atomicity, Theoretical Computer Science 59 (1,2), pp. 25–84, 1988.Google Scholar
  3. [BC89]
    Boudol, G., Castellani, I., Permutations of Transitions: An Event Structure Semantics for CCS, In Proc. REX School, Workshop on Linear Time Branching Time and Partial Orders in Logics and Models for Concurrency, LNCS 354, pp 411–437 1989.Google Scholar
  4. [BC90]
    Boudol, G., Castellani, I., Three Equivalent Semantics Semantics for CCS, In Semantics of Systems of Concurrent Processes, LNCS 469, pp 96–141, 1990.Google Scholar
  5. [BCKH91]
    Boudol, G., Castellani, I., Kiehn, A., Hennessy, M., Observing Localities, To appear Proc. MFCS 1991, LNCS, 1991.Google Scholar
  6. [BHR84]
    Brookes, S.D., Hoare, C.A.R., Roscoe, A.D., A Theory of Communicating Sequential Processes, Journal of ACM 31 (3), pp 560–599, 1984.Google Scholar
  7. [BK84]
    Bergstra, J., Klop, W., Process Algebra for Synchronous Communication, Information and Control 60, pp 109–137, 1984.Google Scholar
  8. [CES86]
    Clarke, E., Emerson, A., Sistla, P. Automatic Verifications of Finite State Concurrent Systems using Temporal Logic Specifications, ACM, TOPLAS, 8, pp 244–263, 1986.Google Scholar
  9. [CFM90]
    Corradini, A., Ferrari, G., Montanari, U. Transition Systems with Algebraic Structure as Models of Computations, In Semantics of Systems of Concurrent Processes, LNCS 469, pp 185–222, 1990.Google Scholar
  10. [DM87]
    Degano, P., Montanari, U., Concurrent Histories: A Basis for Observing Distributed Systems, Journal of Computer and System Sciences 34, pp 422–461, 1987.Google Scholar
  11. [DeS85]
    De Simone, R., Higher Level Synchronising Devices in MEIJE-SCCS, Theoretical Computer Science, 37 (3), pp 245–267, 1985.Google Scholar
  12. [FGM91]
    Ferrari, G., Gorrieri, R., Montanari, U., An Extended Expansion Theorem, In Proc. TAPSOFT 91, LNCS 494, pp 29–48, 1991.Google Scholar
  13. [FM90]
    Ferrari, G., Montanari, U., Towards the Unification of Models for Concurrency, Proc. CAAP'90, LNCS 431, pp 162–176, 1990.Google Scholar
  14. [Ha84]
    Harel, D. Dynamic Logic, In Handbook of Philosophical Logic, Vol II, (Gabbay-Guenthner Eds.), pp 497–604, 1984.Google Scholar
  15. [Ho85]
    Hoare, C.A.R., Communicating Sequential Processes, Prentice Hall, 1985.Google Scholar
  16. [He88]
    Hennessy, M. An Algebraic Theory of Processes, MIT Press, 1988.Google Scholar
  17. [HM85]
    Hennessy, M., Milner, R., Algebraic Laws for Nondeterminism and Concurrency, Journal of ACM 32 (1), pp 137–141, 1985.Google Scholar
  18. [La83]
    Lamport, L. What Good is Temporal Logic, IFIP-83, pp 657–668, 1983.Google Scholar
  19. [Ma77]
    Mazurkiewicz, A. Concurrent Program Schemes and their Interpretations, Technical Report DAIMI PB-78, Aarhus University, 1977.Google Scholar
  20. [Ma89]
    Mazurkiewicz, A. Basic Notions of Trace Theory,In Proc. REX School, Workshop on Linear Time Branching Time and Partial Orders in Logics and Models for Concurrency, LNCS 354, pp 285–363, 1989.Google Scholar
  21. [Mil80]
    Milner, R., A Calculus of Communicating Systems, LNCS 92, 1980.Google Scholar
  22. [Mil81]
    Milner, R. A Modal Characterization of the Observable Machine Behaviour, In Proc. CAAP 81, LNCS 112, pp 25–34, 1981.Google Scholar
  23. [Mil89]
    Milner, R., Communication and Concurrency, Prentice Hall, 1989.Google Scholar
  24. [MP89]
    Manna, Z., Pnueli, A. The Anchored Version of the Temporal Framework, In Proc. REX School, Workshop on Linear Time Branching Time and Partial Orders in Logics and Models for Concurrency, LNCS 354, pp 201–284 1989.Google Scholar
  25. [Par81]
    Park, D., Concurrency and Automata on Infinite Sequences, in Proc. GI, LNCS 104, pp 167–183, 1981.Google Scholar
  26. [NPW81]
    Nielsen, M., Plotkin, G., Winskel, G. Petri Nets, Event Structures and Domains (Part I). Theoretical Computer Science, 13 (1), pp 85–108, 1981.Google Scholar
  27. [Plo81]
    Plotkin, G. A Structured Approach to Operational Semantics, DAIMI FN-19, Computer Science Dept. University of Aarhus, 1981.Google Scholar
  28. [PP90]
    Plotkin, G., Pratt, W., Teams Can See Pomsets, Preliminary Report, August 1990.Google Scholar
  29. [Pr86]
    Pratt, V., Modelling Concurrency with Partial Orders, Int. Journal of Parallel Programming, 15 (1), pp 381–400, 1986.Google Scholar
  30. [Re85]
    Reisig, W. Petri Nets: An Introduction, EATCS Monograph, Springer, 1985.Google Scholar
  31. [Sti89]
    Stirling, C. Modal and Temporal Logics, To appear in Handbook of Logic in Computer Science, Vol I, (Gabbay-Maibaum Eds.) Oxford University Press.Google Scholar
  32. [Win82]
    Winskel, G. Event Structure Semantics for CCS and Related Languages, Proc. ICALP 82, LNCS 140, pp 561–576, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Gian Luigi Ferrari
    • 1
  • Ugo Montanari
    • 2
  1. 1.IEI-CNRItaly
  2. 2.Dipartimento di InformaticaUniversità di PisaItaly

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